{"id":"https://openalex.org/W3115662350","doi":"https://doi.org/10.3390/e23010006","title":"Computing Integrated Information (\u03a6) in Discrete Dynamical Systems with Multi-Valued Elements","display_name":"Computing Integrated Information (\u03a6) in Discrete Dynamical Systems with Multi-Valued Elements","publication_year":2020,"publication_date":"2020-12-22","ids":{"openalex":"https://openalex.org/W3115662350","doi":"https://doi.org/10.3390/e23010006","mag":"3115662350","pmid":"https://pubmed.ncbi.nlm.nih.gov/33375068"},"language":"en","primary_location":{"id":"doi:10.3390/e23010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010006","pdf_url":"https://www.mdpi.com/1099-4300/23/1/6/pdf?version=1609336588","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/1/6/pdf?version=1609336588","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102025610","display_name":"Juan David G\u00f3mez","orcid":"https://orcid.org/0000-0003-3038-3754"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan D. Gomez","raw_affiliation_strings":["Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008945327","display_name":"William G. P. Mayner","orcid":"https://orcid.org/0000-0002-9737-6260"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William G. P. Mayner","raw_affiliation_strings":["Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","Neuroscience Training Program, University of Wisconsin-Madison, Madison, WI 53719, USA"],"raw_orcid":"https://orcid.org/0000-0002-9737-6260","affiliations":[{"raw_affiliation_string":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Neuroscience Training Program, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008697779","display_name":"M. Beheler-Amass","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maggie Beheler-Amass","raw_affiliation_strings":["Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001381023","display_name":"Giulio Tononi","orcid":"https://orcid.org/0000-0002-3892-4087"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giulio Tononi","raw_affiliation_strings":["Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088756569","display_name":"Larissa Albantakis","orcid":"https://orcid.org/0000-0003-1000-9917"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Larissa Albantakis","raw_affiliation_strings":["Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"],"raw_orcid":"https://orcid.org/0000-0003-1000-9917","affiliations":[{"raw_affiliation_string":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088756569"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.8957,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.72626701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"6","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9369999766349792,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6925406455993652},{"id":"https://openalex.org/keywords/python","display_name":"Python (programming language)","score":0.6866278052330017},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6368706822395325},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5784558653831482},{"id":"https://openalex.org/keywords/binary-data","display_name":"Binary data","score":0.4509519934654236},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4260207414627075},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4224473834037781},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.4160307049751282},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.39278167486190796},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37222325801849365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24204587936401367},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20854812860488892},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09219017624855042}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6925406455993652},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.6866278052330017},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6368706822395325},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5784558653831482},{"id":"https://openalex.org/C2779190172","wikidata":"https://www.wikidata.org/wiki/Q4913888","display_name":"Binary data","level":3,"score":0.4509519934654236},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4260207414627075},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4224473834037781},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.4160307049751282},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.39278167486190796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37222325801849365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24204587936401367},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20854812860488892},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09219017624855042},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010006","pdf_url":"https://www.mdpi.com/1099-4300/23/1/6/pdf?version=1609336588","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33375068","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33375068","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7822016","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7822016","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:1df860d01d644094a427af00be4bfd80","is_oa":true,"landing_page_url":"https://doaj.org/article/1df860d01d644094a427af00be4bfd80","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 1, p 6 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/1/6/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23010006","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 1; Pages: 6","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010006","pdf_url":"https://www.mdpi.com/1099-4300/23/1/6/pdf?version=1609336588","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3742687339","display_name":null,"funder_award_id":"UW 133AAG3451","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G5111404570","display_name":null,"funder_award_id":"TWCF0196","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G7970080228","display_name":null,"funder_award_id":"UW 133AAG3451","funder_id":"https://openalex.org/F4320318038","funder_display_name":"Tiny Blue Dot Foundation"}],"funders":[{"id":"https://openalex.org/F4320318038","display_name":"Tiny Blue Dot Foundation","ror":null},{"id":"https://openalex.org/F4320327239","display_name":"Templeton World Charity Foundation","ror":"https://ror.org/00x0z1472"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3115662350.pdf","grobid_xml":"https://content.openalex.org/works/W3115662350.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W151307157","https://openalex.org/W155351735","https://openalex.org/W196929266","https://openalex.org/W1512746852","https://openalex.org/W1554794238","https://openalex.org/W1832461346","https://openalex.org/W1969469858","https://openalex.org/W1989284002","https://openalex.org/W2001024377","https://openalex.org/W2036919025","https://openalex.org/W2046538693","https://openalex.org/W2049846167","https://openalex.org/W2070484080","https://openalex.org/W2088452582","https://openalex.org/W2114900706","https://openalex.org/W2115782725","https://openalex.org/W2160448328","https://openalex.org/W2160939581","https://openalex.org/W2163057446","https://openalex.org/W2242515881","https://openalex.org/W2243427474","https://openalex.org/W2394834952","https://openalex.org/W2436013910","https://openalex.org/W2474388519","https://openalex.org/W2487295360","https://openalex.org/W2514120153","https://openalex.org/W2517431276","https://openalex.org/W2530178105","https://openalex.org/W2619677877","https://openalex.org/W2753865463","https://openalex.org/W2778199599","https://openalex.org/W2779419474","https://openalex.org/W2905540714","https://openalex.org/W2944935347","https://openalex.org/W2963843362","https://openalex.org/W2979723619","https://openalex.org/W2986131527","https://openalex.org/W2989880046","https://openalex.org/W2994254747","https://openalex.org/W3011959288","https://openalex.org/W3034552536","https://openalex.org/W3042911140","https://openalex.org/W3095411193","https://openalex.org/W3098650128","https://openalex.org/W3123069892","https://openalex.org/W6608038781","https://openalex.org/W6683753088","https://openalex.org/W6743611915"],"related_works":["https://openalex.org/W2154693897","https://openalex.org/W104621197","https://openalex.org/W2094988397","https://openalex.org/W2018164323","https://openalex.org/W2018596126","https://openalex.org/W2083580028","https://openalex.org/W1980535114","https://openalex.org/W2063706985","https://openalex.org/W4233766581","https://openalex.org/W2004653872"],"abstract_inverted_index":{"Integrated":[0],"information":[1,22],"theory":[2],"(IIT)":[3],"provides":[4],"a":[5,14,99],"mathematical":[6],"framework":[7,36],"to":[8,33,53,59,70,98,117],"characterize":[9],"the":[10,38,92,119,123],"cause-effect":[11],"structure":[12,121],"of":[13,20,41,45,62,77,82,114,122],"physical":[15],"system":[16,125],"and":[17,72,86,106],"its":[18,57],"amount":[19],"integrated":[21],"(\u03a6).":[23],"An":[24],"accompanying":[25],"Python":[26],"software":[27],"package":[28],"(\"PyPhi\")":[29],"was":[30],"recently":[31],"introduced":[32],"implement":[34],"this":[35],"for":[37,95],"causal":[39,75,96,120],"analysis":[40,97],"discrete":[42],"dynamical":[43],"systems":[44,60],"binary":[46],"elements.":[47,66,128],"Here,":[48],"we":[49,90],"present":[50],"an":[51],"update":[52],"PyPhi":[54],"that":[55],"extends":[56],"applicability":[58],"constituted":[61],"discrete,":[63],"but":[64],"multi-valued":[65,127],"This":[67],"allows":[68],"us":[69],"analyze":[71],"compare":[73],"general":[74],"properties":[76],"random":[78],"networks":[79],"made":[80],"up":[81],"binary,":[83],"ternary,":[84],"quaternary,":[85],"mixed":[87],"nodes.":[88],"Moreover,":[89],"apply":[91],"developed":[93],"tools":[94],"simple":[100],"non-binary":[101],"regulatory":[102],"network":[103],"model":[104],"(p53-Mdm2)":[105],"discuss":[107],"commonly":[108],"used":[109],"binarization":[110],"methods":[111],"in":[112],"light":[113],"their":[115],"capacity":[116],"preserve":[118],"original":[124],"with":[126]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2021-01-05T00:00:00"}
